cc Computational Chemistry 2332-5984 2332-5968 Scientific Research Publishing 10.4236/cc.2026.143004 cc-152970 Article Chemistry Materials Science Theoretical Analysis of the Light Fastness of Reactive Dyes on Cellulose 0000-0002-6747-023X Wojciechowski Krzysztof 1 Institute of Environmental Engineering and Building Installations, Lodz University of Technology, Lodz, Poland

The author declares no conflicts of interest regarding the publication of this paper.

 01 07 2026 07 2026 14 03 55 72 22 06 2026 28 07 2026 31 07 2026 © 2026 by the authors and Scientific Research Publishing Inc. 2026 This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( https://creativecommons.org/licenses/by/4.0/ ). https://doi.org/10.4236/cc.2026.143004

Five selected reactive dyes were used to perform theoretical calculations of photochemical reactivity indicators in electro-(SE) and nucleophilic reactions (SN). The study utilised reactive dyes in which the reactive group is cyanuric chloride, but which differ in their chromophore structure. They belong to the groups of monoazo, disazo and anthraquinone dyes. The influence of changes in these indicators after the formation of the dye-cellulose covalent bond on their light fastness was analyzed. Using the PM3 limit molecular orbital method (MO), the electron density distribution was calculated for dyes in the highest occupied orbital (HOMO) and the lowest unoccupied (LUMO) in the singlet state. These values reflect the tendency towards an electrophilic reaction with a singlet oxygen atom 1O2 or a nucleophilic reaction with the superoxide radical anion

O

2

·−

on atoms in the dye molecule. Reactivity indicators as super delocalization (SE, SN) and electron density distribution in the ground and excited states were calculated. The values of the super delocalization coefficients indicate the activity of sites in the molecules in the oxidation reaction, the resistance of these dyes to photo-oxidation and their influence on the durability of chemical bonds with the cellulose. It was found that the formation of bonds with the cellulose slightly affects the resistance in the electrophilic oxidation reaction, but this effect is significant in the nucleophilic reaction.

 Cellulose Lightfastness Reactive Azo and Anthraquinone Dyes Photochemical Oxidation PM3 Method Electrophilic and Nucleophilic Reaction HOMO and LUMO 1. Introduction

Light fastness of dyed cellulose is one of the most essential features of finished textiles goods. The phenomenon of fading is complex, and many factors, such as the binding of the dye to the cellulose, the chemical structure of the dye, radiation quality, temperature, and humidity, influence it. Dyes of larger sizes usually take longer to initiate fading: it is inversely proportional to the radius of the dye particle due to the chemical layer effect [1]. A covalent bond with the cellulose ensures the coplanarity of the dye molecules. For greater lightfastness, the dye must have a stable aromatic structure and a minimum number of double bonds or reactive substituents. Electron-donating substituents, e.g. −OH, −NH2, etc., accelerate, while electron-accepting groups, e.g., Cl and Br, retard the fading [2]. The total exposure time is also an important parameter; a short exposure gives the dyed textiles enough time to release the energy needed to return to their initial state. The dye molecule interacting with cellulose exhibits p- and n-type semi conductivity, and their reaction time should be short; higher activation energy for fotoconduction favours higher light fastness [3].

When the reactive dye is in monomolecular form and in interaction with cellulose, the light fastness is expected to be identical to that of the dye molecule itself. However, several publications contradict this view [4]-[7]. It was found that reactive dyes bound by a covalent bond show higher lightfastness than, for example, hydrolyzed forms of dyes. This suggests that the covalent bond between the dye and the cellulose facilitates the transfer of energy from the excited state of the dye molecule to the cellulose macromolecule, changing the rate of dye photodegradation [6]. Other studies have concluded that the nature of the dye-cellulose bond (covalent or adsorption) has negligible effect on light fastness [8]. Such different conclusions may result from other research methods. Some tests were performed on a film through which radiation with the dye’s wavelength λmax passed while the dyed fabrics were analyzed visually. In many cases, the covalent bond between cellulose (cotton) and reactive dyes is believed to increase the dyes’ light fastness. However, his conclusion still requires additional research [9][10]. Research on new chemical structures for dyes requires their synthesis, application to a specific material and testing, which is time- and cost-consuming. The results of theoretical calculations carried out for such structures can help reduce the time to evaluate lightfastness without synthesizing and dyeing. In the group of reactive dyes for dyeing cellulose, the most used are symmetric trichloro-triazine derivatives, which react according to the mechanism of nucleophilic substitution. For this reason, five mono-chlorotriazine derivatives reactive dyes with different chromophores were selected for testing.

2. Calculation Methodology

The structures of selected reactive dye molecules and the cellulose molecule model (Cell) were optimized using the semi-empirical quantum-chemical method PM3 [11] with complete optimization of all bond lengths, angles between them and torsion angles HyperChem v.8.0.6, Hyper-Cube Inc).

Calculations were made for dyes and for the cellulose fibre model (Cell) the optimized structures in the ground state using the molecular mechanics method [MM+, RMS gradient 0.02 kcal·mol−1·Å−1 for the dyes-Cell system ([MM+, RMS gradient 0.03 kcal·mol−1·Å−1). After obtaining structure optymised in the ground state by the MM+, the geometry of the molecule was completely optymised by molecular dynamics (MD, runtime 1ps, step size 0.001 ps, simulation temperature 300 K). Finally, the Hartree-Fock Hamiltonian (UMF) was used to calculated configuration interaction (CI) in the gas phase at 25˚C. Next MD and PM3 calculations were performed 3 to 5 times until the lowest standard enthalpy of formation Hf (kcal·mol−1) was constant (0.02 kcal·mol−1 gradient). Singlet ground state energies were calculated for the three electrons in HOMO and LUMO states. The λmax with an optimised design of the dyes was calculated using the ZINDO/S method. Calculations using the molecular orbital method (MO) were performed in the gas phase. Standard enthalpies of formation and energies of the HOMO and LUMO states for all dyes were calculated using the PM3 method. This study focused on calculating the possible sites of attack by an oxidizing agent in an electrophilic or nucleophilic reaction in dye molecules. In this work, calculations of the electron density of orbitals in the lowest ground HOMO level and the excited LUMO state of the dye were performed. Frontier’s molecular orbital theory suggests that the high electron density region in the dye’s HOMO is the site of electrophilic attack by the singlet oxygen 1O2. An area with high electron density in LUMO is where the nucleophilic attack with the superoxide anion radical O 2 · − takes place [12].

It is assumed that the attack of an electrophilic agent occurs when the energy difference ΔE between the LUMO of singlet oxygen and the HOMO of the dye is less than 6 eV [13]. The reactivity of carbon atoms in a dye molecule is measured by superdelocalisation coefficients: SE for electrophilic reactions and SN for nucleophilic reactions. The values of ΣSE and ΣSN illustrate changes in the reactivity of selected atoms before and after they are covalently bonded to a cellulose fibre via cyanuric chloride. ΣE denotes the energy difference between the excited LUMO state and the ground HOMO state, and corresponds to the wavelength of the absorbed visible light, calculated using the ZINDO/S method. The relative tendency of compounds to electrophilic or nucleophilic attack as SE(N)super delocalization is calculated according to formula (1):

S r E ( N ) = f r E ( N ) E HOMO ( LUMO ) ( − a )

where f r E ( N ) is a measure of the ground/excited state electron density on atom r, and a is multiplied to make it dimensionless (−1 eV), which allows comparison of the reactivity of corresponding atoms in different molecules [14]-[17].

The higher these values are, the greater the likelihood of reaction with photodegradable fragments or atoms of the dye molecule by reactive oxygen species (ROS).

 3. Results and Discussion

To carry out the calculations, five reactive dyes were used: two monoazo dyes (derivatives of H acid), 1 diazo dye and 2 anthraquinone derivatives. As a model of the cellulose molecule, a molecule consisting of 3 parts of glucopyranose (Glu)3 = Cellwas used. First, the structure of each dye molecule was optimized using the molecular mechanics method (MM+), followed by the quantum-chemical method PM3. The structure of the Cell was similarly optimized. Such optimized molecules were connected by a covalent bond, and their geometric structure was additionally optimized using the PM3 method (RMS gradient 0.04 kcal·mol−1). Quantum-chemical calculations are carried out in the gas phase to eliminate the influence of the solvent (and also the fibre) on the colour and, consequently, on the performance properties of the dyes. The calculations also omit −SO3H groups, which only affect the water solubility of the dyes; no effect of these groups on lightfastness has been observed. During the calculations, changes in reactivity coefficients were analysed—super delocalization in the reaction of electrophilic oxidation of SE with singlet oxygen 1O2 and nucleophilic SN with the use of O 2 · − superoxide anion radical. The higher the SE or SN values, the faster the reaction on the analyzed atom is. The reactivity and changes for unbound dyes and those chemically bound to the Cell molecule were compared.

Changes in the electron density on the oxygen atom in the binding of the dye to the dyed cellulose with reactive chlorotriazine dyes lead to the formation of covalent bonds as a result of the SN2 nucleophilic reaction between the ionized hydroxyl group (particularly located at the C6 carbon in the methylol group—CH2OH) in the glucopyranose residue with the reactive atom of the dye center, which is the polarized N-Cl bond in chlorotriazine. The formation of a covalent bond between the reactive dye and the Cell (Figure 1) causes changes in the electron density in the cellulose residue and reactive dye.

Figure 1. Model of the “Dye-Cell” adopted for research and calculations.

In the reaction with the reactive dye, the hydroxyl group of the methylol substituent (O1) is reactive. The calculation results are presented in Table 1.

Table 1.Changes in the electron density fH on the O1 oxygen atom after binding the tested reactive dyes with Cell.

Dye RR12 + Cell RR45 + Cell RBr1 + Cell RB2 + Cell RB5 + Cell
f H (O 1) −0.142 −0.138 −0.143 −0.148 −0.136
Δf H (O1) 58.7 59.9 58.4 57.0 60.5

fH(Cell) = −0.344; ΔfH(O1) (%) = (fH(Cell) − fH(O1))/fH(Cell).

These changes concern only the oxygen atom O1, which forms a covalent bond with the cyanuric chloride. All dyes, after forming a covalent bond with the Cell, cause a decrease in the electron density on the oxygen atom O1, and this change is over 50% about the initial value fH(Cell) = −0.344 (Table 1). The highest change occurs for the RB5 dye and the smallest for RB2. On O2 and O2 atoms in the glucopyranose ring, these changes are no greater than 1.7 ÷ 2.6%.

3.1. Calculations for Reactive Red 12 [ <xref ref-type="bibr" rid="B18">18</xref> ]

Figure 2. Model RR12+Cell adopted for research and calculation.

This dye exists in the hydrazone form (Figure 2). The formation of a dye bond with the Cell causes a hypochromic effect of approximately 5 nm (ZINDO/S), which results from changes in the energy of the LUMO level (Table 2).

Table 2. Energy and color changes in HOMO and LUMO of RR12 and RR12+Cell.

RR12 RR12 + Cell
λ max [nm] f λ max [nm] f
PM3 404.5 0.815 395.2 0.733
ZINDO/S 410.7 0.692 406.0 0.644
ΔE 6.8194 6.9274

ΔE = EHOMO – ELUMO kcal·mol−1.

The most susceptible to photooxidation (SE) in RR12(Table 3 and Figure 3) are the carbon atoms C9 (0.0328), C13 (0.0235) and C16 (0.0230). As a result of forming a bond with Cell, the reactivity of the atom C16 (0.0230 → 0.0136) changes significantly, i.e., it decreases by 41.0%. In other cases, they are much smaller and amount to C9 3.87% and C13 8.08%.

Table 3. Theoretical values electron densities (fE, fN) and reactivity (SE, SN) on the most reactive atoms in the RR12 dye and in RR12+Cell after formation of the covalent bond.

RR12 RR12 + Cell
Atom f E S E f E S E
E HOMO = −8.2496 kcal·mol − 1 E HOMO = −8.4034 kcal·mol − 1
9 −0.2705 0.0328 9 −0.2649 0.0315
11 −0.1438 0.0174 11 −0.1415 0.0168
13 −0.1937 0.0235 13 −0.1819 0.0216
16 −0.1897 0.0230 18 −0.1280 0.0152
Σ(S E /f E ) −0.7977 0.0967 Σ(S E /f E ) −0.7163 0.0852
10.20% 11.86%
RR12 RR12 + Cell *
Atom f N S N f N S N
E LUMO = −1.4302 kcal·mol − 1 E LUMO = −1.4760 kcal·mol − 1
7 0.4030 0.2818 7 0.4020 0.2724
14 0.2896 0.2025 14 0.2885 0.1955
19 0.2108 0.1474 19 0.1512 0.1024
22 0.2201 0.1491
26 0.15073 0.1054 26 0.1554 0.1053
Σ(S N /f N ) 1.0541 0.7371 Σ(S N /f N ) 0.9971 0.6755
5.41% 8.36%

*excluding C22.

Figure 3. An example of a graphical presentation of changes in the most reactive atoms of RR12, unbound (open cycle) and bound to Cell (patterned cycle). The size of the circle is proportional to the value of the super delocalization coefficient in the reaction of electrophilic SE or nucleophilic oxidation of SN.

The sum of the super additivity indicators ΣSE for the reactive carbon atoms is 11.86% lower compared to the atoms in reactive dye not bonded to the Cell (Table 3). In the case of RR12 dye, forming a bond with the Cell should increase lightfastness.

In the nucleophilic photooxidation reaction of SN using the superoxide anion radical O 2 · − , the dye binding to the Cell increases the resistance to photooxidation, the lightfastness should be better. The total change in the reactivity ΣSN of the RR12+Cell bound dye compared to the unbound dye is 8.36%. (0.7371 → 0.6755). The most significant change in the value of the delocalization coefficient occurs at the carbon atom C19 and amounts to 30.52%. The most reactive atoms in the SN reaction are C7 (0.2724) and C14 (0.1955).

Also noteworthy is the high reactivity at the carbon atom C22 (0.1491), which forms a covalent bond between the chlorotriazine molecule and Cell. In the case of C7 and C14 atoms, the reaction should lead to a change or disappearance of color because of changes in the dye’s chromophore system, the change at the C22 atom would be responsible for the bond brake between the dye and the cellulose (Table 3 and Table 4).

Table 4. Changes in the super delocalization coefficient SE in the cyanuric chloride ring after binding RR12 dye with Cell.

RR12 - Cy - Cl RR12 - Cy - Cell
ΣS E 0.0972 0.1049
Δ [%] +7.34

Figure 4. Graphical illustration of the changes in the super delocalization coefficient SE in cyanuric chloride ring after binding the RR12 dye to Cell.

Table 4 and Figure 4 presents the changes in the super delocalization coefficient SE in cyanuric chloride ring after binding of the RR12 dye to Cell.

 3.2. Calculations for Reactive Red 45 [ <xref ref-type="bibr" rid="B19">19</xref> ]

Figure 5. Model RR45+Cell adopted for research and calculation.

RR45 dye (Figure 5) is a derivative of H acid and is available in the hydrazone form. Its bonding with the Cell causes the hypochromic effect by 11.2 nm (ZINDO/S) (Table 5).

Table 5. Energy and color changes in HOMO and LUMO of RR45 and RR45+Cell.

RR45 RR45 + Cell
λ max [nm] f λ max [nm] f
PM3 397.3 0.727 396.0 0.707
ZINDO/S 419.9 0.676 408.7 0.638
ΔE 6.8834 6.9060

This is due to the energy reduction of the 1st excited state of LUMO from -1.4083 kcal·mol−1 to −1.4357 kcal·mol−1 (ΔEHOMO-LUMO = 6.8407 kcal·mol−1).

Table 6. Theoretical values electron densities (fE, fN) and reactivity (SE, SN) on selected atoms in the RR45 dye and RR45+Cell after formation of the covalent bond.

RR45 RR45 + Ce ll *
Atom f E S E f E S E
E HOMO = −8.2636 kcal·mol − 1 E HOMO = −8.2764 kcal·mol − 1
2 −0.2739 0.0332 2 −0.2743 0.0331
5 −0.1840 0.0223 5 −0.1906 0.0230
7 −0.1434 0.0174 7 −0.1466 0.0177
11 −0.1303 0.0158 9 −0.1404 0.0170
Σ(S E /f E ) −0.7316 0.0885 Σ(S E /f E ) −0.7519 0.0908
− 2.77% − 2.60%
RR45 RR45 + Cel l *
Atom f N S N f N S N
E LUMO = −1.4083 kcal·mol − 1 E LUMO = −1.4357 kcal·mol − 1
4 0.2879 0.2044 4 0.2896 0.2016
13 0.1568 0.1114 13 0.1680 0.1170
18 0.2203 0.1535
N21 0.4140 0.2940 21 0.4127 0.2874
29 0.1440 0.1022 29 0.1514 0.1054
Σ(S N /f N ) 1.0027 0.7120 Σ(S N /f N ) 1.0215 0.7115
−1.89 % 0.08%

*excluding C18.

RR45 dye has an additional methyl group at the N29 nitrogen atom. The C2 atom (SE = 0.0331) and C5 (SE = 0.0223) have the highest reactivity in the electrophilic photooxidation reaction. Binding to Cell changes these values slightly. The most notable change is observed at C9 carbon atom, by 20.36%. Binding to the Cell means this dye should be more susceptible to reaction with singlet oxygen 1O2. The electrophilic SE photooxidation reaction should occur at the C2 (0.0332) carbon atom and then at the C5 (0.0223) atom. The most notable change in the SE value is observed at the C9 carbon atom, by 15.49%. Changes in the SE value on the remaining atoms susceptible to attack molecule oxygen 1O2 are insignificant and amount to 2% - 3% (Table 6). Finally binding RR45 dye to the Cell causes its lightfastness to decrease in the electrophilic reaction by 2.60% (ΣSE 0.0885 → 0.0908).

Greater changes are observed in the nucleophilic photooxidation of SN using the superoxide anion radical O 2 · − , while N21 (0.2940) and C4 (0.2044) are the most reactive atoms. This type of reaction can also occur at the C18 (0.1535) carbon atom; the effect should be to break the bond with the cellulose, i.e., reduce the resistance to wet factors. Oxidation at C4, C13 and N21 atoms should destroy the chromophore system and the vanishing of the dye’s color. The most extensive changes in the super delocalization coefficient occur on the C13 atom by 5.07%.

In the SN reaction, dye binding with the Cell should cause a slight reduction in the dye’s reactivity to photooxidation by 0.07% (ΣSN), it means that lightfastness should be increased.

Table 7. Changes in the superdelocalization coefficient SE in the cyanuric chloride ring after bonding RR45 dye with Cell.

RR45-Cy-Cl RR45-Cy-Cell
ΣS E 0.0743 0.0886
Δ [%] 16.14

Forming the bond with the cellulose slightly reduces light resistance and oxidizing agent by 16.14% (Table 7). Like in the case of the dye discussed previously, the reactivity of the C18 carbon atom, which is involved in forming a bond with the cellulose, increases significantly (0.1535). The nucleophilic oxidation reaction should occur for RR45+Cell in the following order:

N21 (0.2874) > C4 (0.2016) > C18 (0.1535)

i.e., the dye RR45 should first change its color due to changes in the chromophore system (N21, C4 atom), then undergo bond breaking with the Cell at the C18 atom in a reaction catalyzed by the O 2 · − superoxide radical anion.

 3.3. Calculations for Reactive Brown 1 [18]

Figure 6. Model RBr1+Cell adopted for research and calculation.

Reactive Brown 1 (Figure 6) is a diazo dye. It occurs only in the azo form and is a derivative of 1-Aminonaphthalene-6-sulfonic acid (Cleve acid-1,6). As a result of binding to the cellulose, it should exhibit a bathochromic effect of 4.0 nm (Table8).

Table 8. Energy and color changes in HOMO and LUMO of RR45 and RR45+Cell.

RBr1 RBr1 + Cell
λ max [nm] f λ max [nm] f
PM3 345.8 1.448 357.6 1.245
ZINDO/S 368.4 1.409 372.4 1.402
ΔE 7.2381 7.0545

ΔE = EHOMO − ELUMO [kcal·mol−1].

Table 9. Theoretical values electron densities (fE, fN) and reactivity (SE, SN) on selected atoms in the RBr1 dye and RBr1+Cell after formation of the covalent bond.

RBr1 RBr1 + Ce ll *
Atom f E S E f E S E
E HOMO = −8.5622 kcal·mol − 1 E HOMO = −8.2680 kcal·mol − 1
1 −0.1128 0.0132 1 −0.1116 0.0135
3 −0.1087 0.0127 3 −0.1078 0.0130
24 −0.1035 0.0121 24 −0.1030 0.0125
26 −0.1123 0.0131 26 −0.1082 0.0131
Σ(S E /f E ) −0.4374 0.0511 Σ(S E /f E ) −0.4306 0.0521
1.55% − 1.96%
RBr1 RBr1 + C ell *
Atom f N S N f N S N
E LUMO = −1.3241 kcal·mol − 1 E LUMO = −1.2135 kcal·mol − 1
27 0.2950 0.2228 27 0.4089 0.3369
30 0.2307 0.1901
34 0.1601 0.1209 34 0.1475 0.1215
Σ(S N /f N ) 0.4551 0.3437 Σ(S N /f N ) 0.5563 0.4585
22.24% − 33.40%

*excluding C30.

RBr1 forming bonds with the Cell reduces its resistance in the electrophilic reaction with 1O2 by approximately 1.96% (ΔSE 0.0511 → 0.0521). Changes in reactivity in selected atoms are slight, up to about 3%. The most reactive atoms should be C1 (0.0135) and C26 (0.0131) (Table 8 and Table 9). These values are almost 2.5 times lower than for monoazo dye molecules. At the same time, the superdelocalisation coefficients ΣSE in the cyanuric chloride ring change as shown in Table 10.

In the nucleophilic reaction, the highest reactivity is characterized by the N27 nitrogen atom (0.3369), higher than that of a dye unbonded to Cell by as much as 51.25%. The C30 carbon atom (0.1901) is also characterized by high reactivity. In the SN reaction, the increase in reactivity is ΔSN = −33.40% for the dye bound to the Cell. The calculated values indicate that this dye should have lower lightfastness and wet fastness compared to the previously discussed monoazo dyes.

Table 10. Changes in the super delocalization coefficient SE in the cyanuric chloride ring after bonding RBr1 dye with Cell.

RBr1-Cy-Cll RBr1-Cy-Cell
ΣS E 0.0901 1.1110
Δ [%] +18.82

This dye should undergo bond breaking due to a reaction with superoxide anion radical O 2 · − ; it has a remarkably high SN value on the C30 carbon atom, forming a bond with the cellulose. N27 atoms and N34 are not components of the chromophore system of the dye; the dye should be removed by breaking the bond with Cell.

 3.4. Calculations for Reactive Blue 2 [ <xref ref-type="bibr" rid="B18">18</xref> ] [-rId39-]

Figure 7. Model RB2+Cell adopted for research and calculation.

Table 11. Energy and color changes in HOMO and LUMO of RB2 and RB2+Cell.

RB2 RB2 + Cell
λ max [nm] f λ max [nm] f
PM3 343.7 0.232 332.1 0.205
ZINDO/S 342.9 0.315 335.1 0.310
ΔE 7.0257 7.2132

ΔE = EHOMO – ELUMO [kcal·mol−1].

Cell colored with RB2 should cause the hypochromic effect of 7.8nm (ZINDO/S) because of a significant reduction in the HOMO energy of the dye in the bound state with Cell (Table 11). The formation of a bond with the Cell by RB2 (Figure 7) should reduce its resistance to light in the electrophilic 1O2 reaction by 9.90% (ΔSE 0.0755 → 0.0687). The most reactive carbon atom is C27 (0.0236), followed by C39 (0.0179). On the remaining atoms, the reactivity changes are insignificant ≤ 3% (Table 12).

Table 12. Theoretical values electron densities (fE, fN) and reactivity (SE, SN) on selected atoms in the RB2 dye and RB2+Cell after formation of the covalent bond.

RB2 RB2 + Cel l *
Atom f E S E f E S E
E HOMO = −8.3015 kcal·mol − 1 E HOMO = −8.48610 kcal·mol − 1
27 −0.1868 0.0225 27 −0.2003 0.0236
31 −0.1289 0.0155 31 −0.1437 0.0169
39 −0.1304 0.0157 39 −0.1517 0.0179
41 −0.1239 0.0149 43 −0.1450 0.0171
Σ(S E /f E ) −0.5700 0.0687 Σ(S E /f E ) −0.6407 0.0755
12.40% − 9.96%
RB2 RB2 + Cell *
Atom f N S N f N S N
E LUMO = −1.2757 kcal·mol − 1 E LUMO = −1.2729 kcal·mol − 1
11 0.1984 0.1555 11 0.2114 0.1661
14 0.2299 0.1806
26 0.3314 0.2598 26 0.3275 0.2573
29 0.3611 0.2830 29 0.3692 0.2901
37 0.2716 0.2129 37 0.2372 0.1863
Σ(S N /f N ) 1.1624 0.9111 Σ(S N /f N ) 1.1453 0.8998
1.47% 1.24%

*excluding C14.

Calculations show that the cellulose-bound dye in the process of photodegradation occurring according to SE induces a decrease lightfastness, and according to the SN mechanism, an increase lightfastness (Table 12).

In the nucleophilic reaction, the reaction center is the C29 carbon atom of the anthraquinone set carbonyl group (SE = 0.2901). The increase in reactivity is consumed on the C37 atom by 12.46% (0.2129 → 0.1863). The nucleophilic reaction also produces reactivity at the C14 carbon atom (0.1806), forming a covalent compound with the cyanuric chloride.

The course of photo-oxidation transmission should first result in the discoloration of the dye due to changes in its chromophore system, followed by its breaking bond with Cell and migration from cellulose, e.g., to the dyeing or washing bath (Table 13). Moreover, in the SN reaction, the lightfastness of the dye increases by 1.24% after binding to Cell, calculated in the values of the super additivity coefficients ΣSN.

Table 13. Changes in the super delocalization coefficient SE in the cyanuric chloride ring after bonding RB2 dye with Cell.

RB2-Cy-Cl RB2-Cy-Cell
ΣS E 0.0922 0.1021
Δ [%] +9.69
3.5. Calculations for Reactive Blue 5 [ <xref ref-type="bibr" rid="B18">18</xref> ][20]

Figure 8. Model RB5+Cell adopted for research and calculation.

RB5 dye (Figure 8) is an RB2 isomer in which the cyanuric chloride residue is attached to the anthraquinone dye via m-phenylenediamine (RB2 → p-phenylenediamine). Binding to the Cell causes a small bathochromic effect of 2.0 nm. It results from increasing the energy of the HOMO ground state by 0.0337 kcal·mol−1 and LUMO by 0.0141 kcal·mol−1 (ΔEHOMO-LUMO = 7.0915 kcal·mol−1) (Table 14).

Table 14. Energy and color changes in HOMO and LUMO of RB5 and RB5+Cell.

RB5 RB5 + Cell
λ max [nm] f λ max [nm] f
PM3 337.0 0.178 342.5 0.200
ZINDO/S 336.4 0.271 338.4 0.273
ΔE 7.1112 7.0915

RB5 forming a bond with Cell should reduce lightfastness by 1.28% compared to the dye not bound in the electrophilic reaction with 1O2. The most notable change is observed at the C41 carbon atom by 5.20%.

In the nucleophilic reaction with superoxide radical anion O 2 · − , the formation of a bond with Cell causes a slight deterioration in lightfastness by 15.88% (Table 15) and is subject to change superdelocalisation coefficient ΣSE in cyjanuric ring (Table 16). The highest reactivity is characterized by C31 carbon atom (0.2851) and C28 (0.2849). The C14 atom (0.1846), which forms a bond between the dye and the Cell, is also highly reactive. However, it is lower than the reactivity of the anthraquinone residue.

Table 15.Theoretical values electron densities (fE, fN) and reactivity (SE, SN) on selected atoms in the RB5 dye and RB5+Cell after formation of the covalent bond.

RB5 RB5 + C ell *
Atom f E S E f E S E
E HOMO = −8.3429 kcal·mol − 1 E HOMO = −8.3092 kcal·mol − 1
5 −0.1214 −0.1247 0.0150
29 −0.1780 0.0213 29 −0.1750 0.0211
41 −0.1628 0.0195 41 −0.1538 0.0185
45 −0.1253 0.0150 45 −0.1240 0.0149
Σ(S E /f E ) −0.5875 0.0704 Σ(S E /f E ) −0.5775 0.0695
1.70% 1.28%
RB5 RB5 + Ce ll *
Atom f N S N f N S N
E LUMO = −1.2317 kcal·mol − 1 E LUMO = −1.2176 kcal·mol − 1
11 0.1965 −0.1595 11 0.2008 −0.1649
14 0.2248 −0.1846
28 0.3509 −0.2849 21 0.1689 −0.1387
31 0.3511 −0.2851 28 0.3402 −0.2794
39 0.2908 −0.2361 39 0.2790 −0.2292
Σ(S N /f N ) 1.1892 0.9655 Σ(S N /f N ) 0.9889 0.8122
16.84% 15.88%

*excluding C14.

Table 16. Changes in the super delocalization coefficient SE in the cyanuric chloride ring after bonding RB5 dye with Cell.

RB5-Cy-Cl RB5-Cy-Cell
ΣS E 0.0909 0.1065
Δ [%] +14.64
3.6. Influence of S <sup>E</sup> and S <sup>N</sup> Type Photodegradation on Light Fastness

Computer calculations showed that analyzed dyes and their combinations with Cell behave differently under conditions favoring the electrophilic/nucleophilic reaction using active oxygen compounds, 1O2 and O 2 · − , respectively and proceed in accordance with the reactions considered by other authors [21]-[26]:

dye → light dye * + O 3 2 → electron transfer dye · + + O 2 · −

Although many modelling studies have shown that singlet oxygen 1O2 is very reactive in dyes [21][22], its significance is unclear. Recent work suggests that its role in the photobleaching of azo dyes is relatively small [23][24].

It has also been shown that the quenching of the excited states of dyes by oxygen leads to the formation of the superoxide anion O 2 · − and the destruction of the dye [25]. The formed superoxide anion radical can further react, destroying subsequent dye molecules [26].

The direction and course of the reaction is clearly related to changes in the electron density on the atoms of dye molecules and their superdelocalization in the HOMO and LUMO states. An increase in the reactivity of the molecule with the active form of oxygen means an increase in the photodegradation of the dye, which is equivalent to a decrease in lightfastness. Based on the results, the dyes can be ranked from most to least resistant to photodegradation by electrophilic SE oxidation reaction as follows:

RR12 (+11.89) > RB5 (+1.28) > RBr1 (−1.96) > RR45 (−2.60) > RB2 (−9.90)

In the nucleophilic reaction of SN using the anion-radical O 2 · − , the formation of bonds with the Cell causes changes in the lightfastness as follows:

RB5 (+15.88) > RR12 (+8.35) > RB2 (+1.24) > RR45 (+0.07) > RBr1 (−33.40)

It can be concluded that more sensitive to superoxide anion radical O 2 · − oxidation in the SN reaction are the bonds of anthraquinone derivatives and the diazo dye, while the bonds of monoazo dyes are more stable.

4. Summary

The performed calculations of the lightfastness for five reactive dyes, cyanuric chloride derivatives, not bonded and covalently bonded to cellulose. These dyes belong to the group of monoazo and diazo dyes, and anthraquinones. As cellulose molecule model Cell = (Glu)3 has been used.

Using the PM3 method, the changes in the reactivity indicators for unbound reactive dyes and in the Cell+Dye model were calculated. Calculations were performed for the electrophilic photooxidation reaction of SE with oxygen in the singlet state 1O2 and the nucleophilic reaction of SN with the anion radical O 2 · − .

The calculations SE indices indicate that bond formation with the Cell should slightly reduce light resistance compared to unbound dyes. The performed reactivity comparison for the most reactive atoms in the molecules, determined the sum of the values of the super delocalization coefficients ΣSE.

A similar method was used to calculate the SN indices in the photooxidation reaction according to the nucleophilic mechanism using the O 2 · − anion radical.

An increase in the reactivity of the molecule with the active form of oxygen means an increase in the photodegradation of the dye, which is equivalent to a decrease in lightfastness. The calculations indicate that bond formation with the Cell should slightly reduce lightfastness comparing to unbound dyes.

The calculations indicate that the PM3 method can predict the sites of electrophilic and nucleophilic attack of the oxygen molecule on the reactive dye bound with Cell by a covalent bond. This method has not been used before for this type of calculations and allows the analysis of dyes resistance to light to be extended with numerical methods. They can complement the comparative analysis based on the grey scale used in textile practice.

 References Giles, C.H. (1957) The Light Fastness of Dyed Fibres—A Statistical Study. JournaloftheSocietyofDyersandColourists, 73, 127-160. https://doi.org/10.1111/j.1478-4408.1957.tb02185.x 10.1111/j.1478-4408.1957.tb02185.xhttps://doi.org/10.1111/j.1478-4408.1957.tb02185.x Giles, C.H. 1957 The Light Fastness of Dyed Fibres—A Statistical Study Journal of the Society of Dyers and Colourists 73 10.1111/j.1478-4408.1957.tb02185.x Clark, M. (2011) Handbook of Textile and Industrial Dyeing. Woodhead Publishing Ltd, 211-223. https://doi.org/10.1533/9780857094919 10.1533/9780857094919https://doi.org/10.1533/9780857094919 Clark, M. 2011 Handbook of Textile and Industrial Dyeing Woodhead Publishing Ltd 211 10.1533/9780857094919 Horton, F.J., Patterson, D. and Rizzo, F.J. (1976) Photoconductivity and Fading. I. The Dyes Used in the ISO Light-Fastness Test. JournaloftheSocietyofDyersandColourists, 92, 269-272. https://doi.org/10.1111/j.1478-4408.1976.tb03292.x 10.1111/j.1478-4408.1976.tb03292.xhttps://doi.org/10.1111/j.1478-4408.1976.tb03292.x Horton, F.J. Patterson, D. Rizzo, F.J. 1976 Photoconductivity and Fading I. The Dyes Used in the ISO Light-Fastness Test. Journal of the Society of Dyers and Colourists 92 10.1111/j.1478-4408.1976.tb03292.x Baranova, G.S., Romanova, M.G. and Chekalin, M.A. (1972) Fading of Reactive Dyes. Textil’naâ Promyŝlennost, 32, 70-71. Baranova, G.S. Romanova, M.G. Chekalin, M.A. 1972 Fading of Reactive Dyes Textil’naâ Promyŝlennost 32 Ingamells, W. (1963) The Enhanced Fading of Dyes Caused by Crease-Resist Resins: A Proposed Mechanism. Journal of the Society of Dyers and Colourists, 79, 651-660. https://doi.org/10.1111/j.1478-4408.1963.tb02525.x 10.1111/j.1478-4408.1963.tb02525.xhttps://doi.org/10.1111/j.1478-4408.1963.tb02525.x Ingamells, W. 1963 The Enhanced Fading of Dyes Caused by Crease-Resist Resins: A Proposed Mechanism Journal of the Society of Dyers and Colourists 79 10.1111/j.1478-4408.1963.tb02525.x Daruwalla, E.H. (1974) Physical Chemistry of Dyeing: State of Dye in Dyebath and in Substrate. In: The Chemistry of Synthetic Dyes, Elsevier, 69-113. https://doi.org/10.1016/b978-0-12-717007-7.50010-x 10.1016/b978-0-12-717007-7.50010-xhttps://doi.org/10.1016/b978-0-12-717007-7.50010-x Daruwalla, E.H. Dyes, E 1974 Physical Chemistry of Dyeing: State of Dye in Dyebath and in Substrate In: The Chemistry of Synthetic Dyes 69 10.1016/b978-0-12-717007-7.50010-x Zakharova T.D., Soloveva V.B. and Zaitseva V.N. (1971) Influence of Covalent Bonding between Reactive Dyes and Cellulose in Fibers on Light Fastness of the Dyes. ZhurnalPrikladnoiKhimii, 44, 2771-2773. 1971 Influence of Covalent Bonding between Reactive Dyes and Cellulose in Fibers on Light Fastness of the Dyes Zhurnal Prikladnoi Khimii 44 Krichevsk, G.E., Vachobov, B., Ershov, Y.A. and Dovb, E.B. (1975) Lightfastness of Reactive Dyes. TextileResearchJournal, 45, 608-619. https://doi.org/10.1177/004051757504500809 10.1177/004051757504500809https://doi.org/10.1177/004051757504500809 Krichevsk, G.E. Vachobov, B. Ershov, Y.A. Dovb, E.B. 1975 Lightfastness of Reactive Dyes Textile Research Journal 45 10.1177/004051757504500809 Stephen, W.E. (1965) The Early Work on Reactive Dyes for Cellulose. Chimia, 19, 261. https://doi.org/10.2533/chimia.1965.261 10.2533/chimia.1965.261https://doi.org/10.2533/chimia.1965.261 Stephen, W.E. 1965 The Early Work on Reactive Dyes for Cellulose Chimia 19 10.2533/chimia.1965.261 Rattee, I.D. (1984) Reactive Dyes for Cellulose 1953-1983. Review of Progress in Coloration and Related Topics, 14, 50-57. https://doi.org/10.1111/j.1478-4408.1984.tb00044.x 10.1111/j.1478-4408.1984.tb00044.xhttps://doi.org/10.1111/j.1478-4408.1984.tb00044.x Rattee, I.D. 1984 Reactive Dyes for Cellulose 1953-1983 Review of Progress in Coloration and Related Topics 14 10.1111/j.1478-4408.1984.tb00044.x Stewart, J.J.P. (1989) Optimization of Parameters for Semiempirical Methods I. Method. JournalofComputationalChemistry, 10, 209-220. https://doi.org/10.1002/jcc.540100208 10.1002/jcc.540100208https://doi.org/10.1002/jcc.540100208 Stewart, J.J.P. 1989 Optimization of Parameters for Semiempirical Methods I Method. Journal of Computational Chemistry 10 10.1002/jcc.540100208 Morita, Z. and Hada, S. (1999) A Semiempirical Molecular Orbital Study on the Reaction of an Aminopyrazolinyl Azo Dye with Singlet Molecular Oxygen. DyesandPigments, 41, 1-10. https://doi.org/10.1016/s0143-7208(98)00038-2 10.1016/s0143-7208(98)00038-2https://doi.org/10.1016/s0143-7208(98)00038-2 Morita, Z. Hada, S. 1999 A Semiempirical Molecular Orbital Study on the Reaction of an Aminopyrazolinyl Azo Dye with Singlet Molecular Oxygen Dyes and Pigments 7208 98 10.1016/s0143-7208(98)00038-2 Wang, L., Wang, X. and Zhang, H. (2005) A Theoretical Study on Photobleaching Mechanisms of Hypocrellins. DyesandPigments, 67, 161-166. https://doi.org/10.1016/j.dyepig.2004.11.007 10.1016/j.dyepig.2004.11.007https://doi.org/10.1016/j.dyepig.2004.11.007 Wang, L. Wang, X. Zhang, H. 2005 A Theoretical Study on Photobleaching Mechanisms of Hypocrellins Dyes and Pigments 67 10.1016/j.dyepig.2004.11.007 Guo, L., Meng, F.S., Gong, X.D., Xiao, H.M., Chen, K.C. and Tian, H. (2001) Synthesis and Spectral Properties of Soluble Trimethylsilyl Substituted Metal-Phthalocyanines. DyesandPigments, 49, 83-91. https://doi.org/10.1016/s0143-7208(01)00011-0 10.1016/s0143-7208(01)00011-0https://doi.org/10.1016/s0143-7208(01)00011-0 Guo, L. Meng, F.S. Gong, X.D. Xiao, H.M. Chen, K.C. Tian, H. 2001 Synthesis and Spectral Properties of Soluble Trimethylsilyl Substituted Metal-Phthalocyanines Dyes and Pigments 7208 01 10.1016/s0143-7208(01)00011-0 Fukui, K., Kato, H. and Yonezawa, T. (1961) “Frontier Electron Density” in Saturated Hydrocarbons. BulletinoftheChemicalSocietyofJapan, 34, 442-445. https://doi.org/10.1246/bcsj.34.442 10.1246/bcsj.34.442https://doi.org/10.1246/bcsj.34.442 Fukui, K. Kato, H. Yonezawa, T. 1961 “Frontier Electron Density” in Saturated Hydrocarbons Bulletin of the Chemical Society of Japan 34 10.1246/bcsj.34.442 Fukui, K., Nagata, C. and Yonezawa, T. (1958) Electronic Structure and Auxin Activity of Benzoic Acid Derivatives. JournaloftheAmericanChemicalSociety, 80, 2267-2270. https://doi.org/10.1021/ja01542a058 10.1021/ja01542a058https://doi.org/10.1021/ja01542a058 Fukui, K. Nagata, C. Yonezawa, T. 1958 Electronic Structure and Auxin Activity of Benzoic Acid Derivatives Journal of the American Chemical Society 80 10.1021/ja01542a058 Wojciechowski, K. and Szuster, L. (2020) Prediction of Photofading of n- β-Hydroxyethylamino- o-Nitrophenyl Derivatives: A Theoretical Study. ColorationTechnology, 137, 134-144. https://doi.org/10.1111/cote.12517 10.1111/cote.12517https://doi.org/10.1111/cote.12517 Wojciechowski, K. Szuster, L. 2020 Prediction of Photofading of n-β-Hydroxyethylamino-o-Nitrophenyl Derivatives: A Theoretical Study Coloration Technology 137 10.1111/cote.12517 Panchartek, J., Allan, Z.J. and Mužík, F. (1960) Aromatische Diazo-und Azoverbindungen XXXIX. Chromatographische Konstitutionsanalyse synthetischer Farbstoffe. CollectionofCzechoslovakChemicalCommunications, 25, 2783-2799. https://doi.org/10.1135/cccc19602783 10.1135/cccc19602783https://doi.org/10.1135/cccc19602783 Panchartek, J. Allan, Z.J. 1960 Aromatische Diazo-und Azoverbindungen XXXIX Chromatographische Konstitutionsanalyse synthetischer Farbstoffe. Collection of Czechoslovak Chemical Communications 25 10.1135/cccc19602783 Mihret, T., Gabbiye, N., Tegegne, B., Tibebe, D. and Alemu, A. (2025) Removal of Reactive Red 45 Dye from Aqueous Solution Using Activated Carbon Developed from Catha Edulis Stem as a Potential Biosorbent. Scientific Reports, 15, Article 28195. https://doi.org/10.1038/s41598-025-09956-2 10.1038/s41598-025-09956-240751054https://doi.org/10.1038/s41598-025-09956-2 Mihret, T. Gabbiye, N. Tegegne, B. Tibebe, D. Alemu, A. 2025 Removal of Reactive Red 45 Dye from Aqueous Solution Using Activated Carbon Developed from Catha Edulis Stem as a Potential Biosorbent Scientific Reports 15 28195 10.1038/s41598-025-09956-2 40751054 Stamm, O.A., Zollinger, H., Zähner, H. and Gäumann, E. (1961) Die Bindung zwischen Reaktivfarbstoff und Cellulose. 7. Mitteilung über textilchemische Untersuchungen. HCA, 44, 1123-1125. https://doi.org/10.1002/hlca.19610440432 10.1002/hlca.19610440432https://doi.org/10.1002/hlca.19610440432 Stamm, O.A. Zollinger, H. 1961 Die Bindung zwischen Reaktivfarbstoff und Cellulose 7. Mitteilung über textilchemische Untersuchungen. HCA 44 10.1002/hlca.19610440432 Wilkinson, F., Helman, W.P. and Ross, A.B. (1995) Rate Constants for the Decay and Reactions of the Lowest Electronically Excited Singlet State of Molecular Oxygen in Solution. an Expanded and Revised Compilation. JournalofPhysicalandChemicalReferenceData, 24, 663-677. https://doi.org/10.1063/1.555965 10.1063/1.555965https://doi.org/10.1063/1.555965 Wilkinson, F. Helman, W.P. Ross, A.B. 1995 Rate Constants for the Decay and Reactions of the Lowest Electronically Excited Singlet State of Molecular Oxygen in Solution an Expanded and Revised Compilation. Journal of Physical and Chemical Reference Data 24 10.1063/1.555965 Griffiths, J. and Hawkins, C. (1977) Oxidation by Singlet Oxygen of Arylazonaphthols Exhibiting Azo-Hydrazone Tautomerism. Journal of the Chemical Society, Perkin Transactions2, 6, 747-752. https://doi.org/10.1039/p29770000747 10.1039/p29770000747https://doi.org/10.1039/p29770000747 Griffiths, J. Hawkins, C. Society, P 1977 Oxidation by Singlet Oxygen of Arylazonaphthols Exhibiting Azo-Hydrazone Tautomerism Journal of the Chemical Society 6 10.1039/p29770000747 Jansen, L.M.G., Wilkes, I.P., Wilkinson, F. and Worrall, D.R. (1999) The Role of Singlet Molecular Oxygen in the Photodegradation of 1-Arylazo-2-Naphthols in Methanol and on Cotton. JournalofPhotochemistryandPhotobiologyA: Chemistry, 125, 99-106. https://doi.org/10.1016/s1010-6030(99)00095-7 10.1016/s1010-6030(99)00095-7https://doi.org/10.1016/s1010-6030(99)00095-7 Jansen, L.M.G. Wilkes, I.P. Wilkinson, F. Worrall, D.R. 1999 The Role of Singlet Molecular Oxygen in the Photodegradation of 1-Arylazo-2-Naphthols in Methanol and on Cotton Journal of Photochemistry and Photobiology A: Chemistry 6030 99 10.1016/s1010-6030(99)00095-7 Yamaguchi, S. and Sasaki, Y. (2001) Spectroscopic Determination of Very Low Quantum Yield of Singlet Oxygen Formation Photosensitized by Industrial Dyes. JournalofPhotochemistryandPhotobiologyA: Chemistry, 142, 47-50. https://doi.org/10.1016/s1010-6030(01)00470-1 10.1016/s1010-6030(01)00470-1https://doi.org/10.1016/s1010-6030(01)00470-1 Yamaguchi, S. Sasaki, Y. 2001 Spectroscopic Determination of Very Low Quantum Yield of Singlet Oxygen Formation Photosensitized by Industrial Dyes Journal of Photochemistry and Photobiology A: Chemistry 6030 01 10.1016/s1010-6030(01)00470-1 Bandara, J. and Kiwi, J. (1999) Fast Kinetic Spectroscopy, Decoloration and Production of H 2O 2 Induced by Visible Light in Oxygenated Solutions of the Azo Dye Orange II. NewJournalofChemistry, 23, 717-724. https://doi.org/10.1039/a902425e 10.1039/a902425ehttps://doi.org/10.1039/a902425e Bandara, J. Kiwi, J. Spectroscopy, D 1999 Fast Kinetic Spectroscopy, Decoloration and Production of H2O2 Induced by Visible Light in Oxygenated Solutions of the Azo Dye Orange II New Journal of Chemistry 23 10.1039/a902425e Batchelor, S.N., Carr, D., Coleman, C.E., Fairclough, L. and Jarvis, A. (2003) The Photofading Mechanism of Commercial Reactive Dyes on Cotton. DyesandPigments, 59, 269-275. https://doi.org/10.1016/s0143-7208(03)00118-9 10.1016/s0143-7208(03)00118-9https://doi.org/10.1016/s0143-7208(03)00118-9 Batchelor, S.N. Carr, D. Coleman, C.E. Fairclough, L. Jarvis, A. 2003 The Photofading Mechanism of Commercial Reactive Dyes on Cotton Dyes and Pigments 7208 03 10.1016/s0143-7208(03)00118-9